Basic Graphing Techniques Algebra Review Basic Graphing Techniques 4/6/99 Graphing Techniques

Graphing Equations The graph of an equation consists of all the points which satisfy or solve the equation. Solve the equation to find the points, then plot the points. These points are called coordinates. Each point (coordinate) consists of one value for y and one value for x, and is written as the ordered pair (x, y). The values of (x, y) solve the equation y = x + c, where c represents a constant value The coordinates are ordered pairs of real numbers. 4/6/99 Graphing Techniques

Variables of an Equation x and y are most commonly used as variables in an equation Variables are placeholders for values Variable y is dependent on the variable x The independent variable, x, is plotted along the horizontal axis (x axis) The dependent variable, y, is plotted along the vertical axis (y axis) 4/6/99 Graphing Techniques

Solve for Ordered Pairs Consider the linear equation y = x + 2 The y value is dependent on the value of x Find ordered pairs by assigning any value to x Let x = 0 and solve for y to find (0, y) y = 0 + 2 or y = 2 The ordered pair is (0, 2) Let x = 1 and solve again for y to find (1, y) y = 1 + 2 or y = 3 The ordered pair is (1, 3) Let x = -2 and solve again for y to find (-2, y) y = -2 + 2 or y = 0 The ordered pair is (-2, 0) 4/6/99 Graphing Techniques

Table and Graph for Ordered Pairs Solutions for y = x + 2 put in a table form x y 0 2 1 3 -2 0 -1 1 Graph of y = x + 2 4/6/99 Graphing Techniques

Types of Graphs y = 2x + 3 is the graph of a straight line y = 2x2 + 3 is the graph of a curved line called a parabola y2 = 2x2 + 3 and y = x3 + 3 are also curved line graphs Graphs are drawn by solving the equations and plotting the ordered pairs. Draw the simplest graph you can to connect all the points. 4/6/99 Graphing Techniques